/*=========================================================================

  Program:   Visualization Toolkit
  Module:    TestInterpolationDerivs.cxx

  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
  All rights reserved.
  See Copyright.txt or http://www.kitware.com/Copyright.htm for details.

     This software is distributed WITHOUT ANY WARRANTY; without even
     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
     PURPOSE.  See the above copyright notice for more information.

=========================================================================*/
#define VTK_EPSILON 1e-10

#include <vtkCellArray.h>
#include "vtkLagrangeTetra.h"
#include <vtkMinimalStandardRandomSequence.h>
#include "vtkPoints.h"
#include "vtkSmartPointer.h"

#include "vtkClipDataSet.h"
#include "vtkDataSetSurfaceFilter.h"
#include "vtkDoubleArray.h"
#include "vtkPointData.h"
#include "vtkPolyData.h"
#include "vtkUnstructuredGrid.h"

#define VISUAL_DEBUG 1

#ifdef VISUAL_DEBUG
#include <vtkVersion.h>
#include <vtkCamera.h>
#include <vtkPolyData.h>
#include <vtkPolyDataMapper.h>
#include <vtkActor.h>
#include <vtkProperty.h>
#include <vtkRegressionTestImage.h>
#include <vtkRenderWindow.h>
#include <vtkRenderer.h>
#include <vtkRenderWindowInteractor.h>
#endif

// #define DEBUG_POINTS

#ifdef DEBUG_POINTS
#include <vtkNew.h>
#include <vtkPolyData.h>
#include <vtkXMLPolyDataWriter.h>
#endif

#include <cassert>

#include <cmath>

namespace
{
vtkSmartPointer<vtkLagrangeTetra> CreateTetra(int nPoints)
{
  vtkSmartPointer<vtkLagrangeTetra> t =
    vtkSmartPointer<vtkLagrangeTetra>::New();

  t->GetPointIds()->SetNumberOfIds(nPoints);
  t->GetPoints()->SetNumberOfPoints(nPoints);
  t->Initialize();
  double* points = t->GetParametricCoords();
  for (vtkIdType i=0;i<nPoints;i++)
    {
      t->GetPointIds()->SetId(i,i);
      t->GetPoints()->SetPoint(i,&points[3*i]);
    }

  return t;
}

int TestInterpolationFunction(vtkSmartPointer<vtkLagrangeTetra> cell,
                              double eps = VTK_EPSILON)
{
  int numPts = cell->GetNumberOfPoints();
  double *sf = new double[numPts];
  double *coords = cell->GetParametricCoords();
  int r = 0;
  for(int i=0;i<numPts;++i)
    {
    double *point = coords + 3*i;
    double sum = 0.;
    cell->InterpolateFunctions(point, sf); // virtual function
    for(int j=0;j<numPts;j++)
      {
      sum += sf[j];
      if(j == i)
        {
        if( fabs(sf[j] - 1) > eps)
          {
          std::cout << "fabs(sf[" << j << "] - 1): " << fabs(sf[j] - 1) << std::endl;
          ++r;
          }
        }
      else
        {
        if( fabs(sf[j] - 0) > eps )
          {
          std::cout << "fabs(sf[" << j << "] - 0): " << fabs(sf[j] - 0) << std::endl;
          ++r;
          }
        }
      }
    if( fabs(sum - 1) > eps )
      {
        std::cout<<"fabs("<<sum<<" - 1): "<<fabs(sum - 1)<<std::endl;
      ++r;
      }
    }

  // Let's test unity condition on the center point:
  double center[3];
  cell->GetParametricCenter(center);
  cell->InterpolateFunctions(center, sf); // virtual function
  double sum = 0.;
  for(int j=0;j<numPts;j++)
    {
    sum += sf[j];
    }
  if( fabs(sum - 1) > eps )
    {
      std::cout<<"center: fabs("<<sum<<" - 1): "<<fabs(sum - 1)<<std::endl;
    ++r;
    }

  delete[] sf;
  return r;
}

void InterpolateDerivsNumeric(vtkSmartPointer<vtkLagrangeTetra> cell,
                              double pcoords[3],
                              double* derivs,
                              double eps = VTK_EPSILON)
{
  vtkIdType nPoints = cell->GetPoints()->GetNumberOfPoints();
  double* valp = new double[nPoints];
  double* valm = new double[nPoints];

  double pcoordsp[3], pcoordsm[3];

  for (vtkIdType i=0;i<3;i++)
    {
    pcoordsp[i] = pcoordsm[i] = pcoords[i];
    }
  pcoordsp[0] += eps;
  cell->InterpolateFunctions(pcoordsp,valp);

  pcoordsm[0] -= eps;
  cell->InterpolateFunctions(pcoordsm,valm);

  for (vtkIdType idx = 0; idx < nPoints; idx++)
    {
      derivs[idx] = (valp[idx] - valm[idx])/(2.*eps);
    }

  for (vtkIdType i=0;i<3;i++)
    {
    pcoordsp[i] = pcoordsm[i] = pcoords[i];
    }
  pcoordsp[1] += eps;
  cell->InterpolateFunctions(pcoordsp,valp);

  pcoordsm[1] -= eps;
  cell->InterpolateFunctions(pcoordsm,valm);

  for (vtkIdType idx = 0; idx < nPoints; idx++)
    {
      derivs[nPoints + idx] = (valp[idx] - valm[idx])/(2.*eps);
    }

  if (cell->GetCellDimension() == 3)
    {
    for (vtkIdType i=0;i<3;i++)
      {
      pcoordsp[i] = pcoordsm[i] = pcoords[i];
      }
    pcoordsp[2] += eps;
    cell->InterpolateFunctions(pcoordsp,valp);

    pcoordsm[2] -= eps;
    cell->InterpolateFunctions(pcoordsm,valm);

    for (vtkIdType idx = 0; idx < nPoints; idx++)
      {
      derivs[2*nPoints + idx] = (valp[idx] - valm[idx])/(2.*eps);
      }
    }

  delete [] valp;
  delete [] valm;
}

int TestInterpolationDerivs(vtkSmartPointer<vtkLagrangeTetra> cell,
                            double eps = VTK_EPSILON)
{
  int numPts = cell->GetNumberOfPoints();
  int dim = cell->GetCellDimension();
  double *derivs = new double[dim*numPts];
  double *derivs_n = new double[dim*numPts];
  double *coords = cell->GetParametricCoords();
  int r = 0;
  for(int i=0;i<numPts;++i)
    {
    double *point = coords + 3*i;
    double sum = 0.;
    cell->InterpolateDerivs(point, derivs);
    InterpolateDerivsNumeric(cell, point, derivs_n, 1.e-10);
    for(int j=0;j<dim*numPts;j++)
      {
      sum += derivs[j];
      if (fabs(derivs[j]-derivs_n[j]) >
          1.e-5*(fabs(derivs[j]) > numPts ? fabs(derivs[j]) : numPts))
        {
          std::cout<<j<<" is different from numeric! "<<derivs[j]<<" "<<derivs_n[j]<<" "<<fabs(derivs[j]-derivs_n[j])<<std::endl;
        ++r;
        }
      }
    if( fabs(sum) > eps*numPts )
      {
        std::cout<<"nonzero! "<<sum<<std::endl;
      ++r;
      }
    }

  // Let's test zero condition on the center point:
  double center[3];
  cell->GetParametricCenter(center);
  cell->InterpolateDerivs(center, derivs);
  double sum = 0.;
  for(int j=0;j<dim*numPts;j++)
    {
    sum += derivs[j];
    }
  if( fabs(sum) > eps )
    {
      std::cout<<"center: nonzero!"<<std::endl;
    ++r;
    }

  delete[] derivs;
  delete[] derivs_n;
  return r;
}

void ViewportRange(int testNum,double* range)
{
  range[0] = .25*(testNum%4);
  range[1] = range[0] + .25;
  range[2] = .25*(testNum/4);
  range[3] = range[2] + .25;
}

void RandomCircle(vtkMinimalStandardRandomSequence* sequence,
                  double radius,
                  double* offset,
                  double* value)
{
  double theta = 2.*vtkMath::Pi()*sequence->GetValue();
  sequence->Next();
  value[0] = radius*cos(theta) + offset[0];
  value[1] = radius*sin(theta) + offset[1];
}

void RandomSphere(vtkMinimalStandardRandomSequence* sequence,
                  double radius,
                  double* offset,
                  double* value)
{
  double theta = 2.*vtkMath::Pi()*sequence->GetValue();
  sequence->Next();
  double phi = vtkMath::Pi()*sequence->GetValue();
  sequence->Next();
  value[0] = radius*cos(theta)*sin(phi) + offset[0];
  value[1] = radius*sin(theta)*sin(phi) + offset[1];
  value[2] = radius*cos(phi) + offset[2];
}

static int testNum = 0;

vtkIdType IntersectWithCell(unsigned nTest,
                            vtkMinimalStandardRandomSequence* sequence,
                            bool threeDimensional,
                            double radius,
                            double* offset,
                            vtkCell* cell
#ifdef VISUAL_DEBUG
                            ,vtkSmartPointer<vtkRenderWindow> renderWindow
#endif
                            )
{
  double p[2][3];
  p[0][2] = p[1][2] = 0.;
  double tol = 1.e-7;
  double t;
  double intersect[3];
  double pcoords[3];
  int subId;
  vtkIdType counter = 0;

  vtkSmartPointer<vtkPoints> points = vtkSmartPointer<vtkPoints>::New();
  vtkSmartPointer<vtkCellArray> vertices = vtkSmartPointer<vtkCellArray>::New();

  for (unsigned i=0;i<nTest;i++)
    {
    if (threeDimensional)
      {
      RandomSphere(sequence,radius,offset,p[0]);
      RandomSphere(sequence,radius,offset,p[1]);
      }
    else
      {
      RandomCircle(sequence,radius,offset,p[0]);
      RandomCircle(sequence,radius,offset,p[1]);
      }

    if (cell->IntersectWithLine(p[0],p[1],tol,t,intersect,pcoords,subId))
      {
      counter++;
      vtkIdType pid = points->InsertNextPoint(intersect);
      vertices->InsertNextCell(1,&pid);
      }
    }

#ifdef DEBUG_POINTS
    {
    vtkSmartPointer<vtkLagrangeTetra> t = CreateTetra(10);
    vtkNew<vtkPolyData> p;
    p->SetPoints(points);
    p->SetVerts(vertices);
    vtkNew<vtkXMLPolyDataWriter> w;
    w->SetFileName("intersection.vtp");
    w->SetInputData(p.GetPointer());
    w->Write();
    }
#endif

#ifdef VISUAL_DEBUG
  vtkSmartPointer<vtkCamera> camera = vtkSmartPointer<vtkCamera>::New();
  camera->SetPosition(2, 2, 2);
  camera->SetFocalPoint(offset[0],offset[1],offset[2]);

  vtkSmartPointer<vtkRenderer> renderer = vtkSmartPointer<vtkRenderer>::New();
  renderer->SetActiveCamera(camera);
  renderWindow->AddRenderer(renderer);
  double dim[4];
  ViewportRange(testNum++,dim);
  renderer->SetViewport(dim[0],dim[2],dim[1],dim[3]);

  vtkSmartPointer<vtkPolyData> point = vtkSmartPointer<vtkPolyData>::New();

  point->SetPoints(points);
  point->SetVerts(vertices);

  vtkSmartPointer<vtkPolyDataMapper> mapper = vtkSmartPointer<vtkPolyDataMapper>::New();
  mapper->SetInputData(point);

  vtkSmartPointer<vtkActor> actor = vtkSmartPointer<vtkActor>::New();
  actor->SetMapper(mapper);
  renderer->AddActor(actor);
  renderer->ResetCamera();

  renderWindow->Render();
#endif

  return counter;
}

vtkIdType TestClip(vtkCell* cell
#ifdef VISUAL_DEBUG
                            ,vtkSmartPointer<vtkRenderWindow> renderWindow
#endif
                            )

{
  vtkSmartPointer<vtkUnstructuredGrid> unstructuredGrid =
    vtkSmartPointer<vtkUnstructuredGrid>::New();
  unstructuredGrid->SetPoints(cell->GetPoints());

  vtkSmartPointer<vtkCellArray> cellArray =
    vtkSmartPointer<vtkCellArray>::New();
  cellArray->InsertNextCell(cell);
  unstructuredGrid->SetCells(cell->GetCellType(), cellArray);

  vtkSmartPointer<vtkDoubleArray> radiant =
    vtkSmartPointer<vtkDoubleArray>::New();
  radiant->SetName("Distance from Origin");
  radiant->SetNumberOfTuples(cell->GetPointIds()->GetNumberOfIds());

  double maxDist = 0.;
  for (vtkIdType i = 0; i < cell->GetPointIds()->GetNumberOfIds();i++)
    {
    double xyz[3];
    cell->GetPoints()->GetPoint(i,xyz);
    double dist = sqrt(xyz[0]*xyz[0] + xyz[1]*xyz[1] + xyz[2]*xyz[2]);
    radiant->SetTypedTuple(i, &dist);
    maxDist = (dist > maxDist ? dist : maxDist);
    }

  unstructuredGrid->GetPointData()->AddArray(radiant);
  unstructuredGrid->GetPointData()->SetScalars(radiant);

  vtkSmartPointer<vtkClipDataSet> clip =
    vtkSmartPointer<vtkClipDataSet>::New();
  clip->SetValue(maxDist*.5);
  clip->SetInputData(unstructuredGrid);

  vtkSmartPointer<vtkDataSetSurfaceFilter> surfaceFilter =
    vtkSmartPointer<vtkDataSetSurfaceFilter>::New();
  surfaceFilter->SetInputConnection(clip->GetOutputPort());
  surfaceFilter->Update();
  vtkPolyData* polydata = surfaceFilter->GetOutput();

#ifdef VISUAL_DEBUG
  vtkSmartPointer<vtkCamera> camera =
    vtkSmartPointer<vtkCamera>::New();
  camera->SetPosition(-2.*maxDist, -2.*maxDist, -2.*maxDist);
  camera->SetFocalPoint(0, 0, 0);

  vtkSmartPointer<vtkRenderer> renderer = vtkSmartPointer<vtkRenderer>::New();
  renderer->SetActiveCamera(camera);
  renderWindow->AddRenderer(renderer);
  double dim[4];
  ViewportRange(testNum++,dim);
  renderer->SetViewport(dim[0],dim[2],dim[1],dim[3]);

  vtkSmartPointer<vtkPolyDataMapper> mapper =
    vtkSmartPointer<vtkPolyDataMapper>::New();
  mapper->SetInputData(polydata);
  mapper->SetScalarRange(maxDist*.5,maxDist);

  vtkSmartPointer<vtkActor> actor =
    vtkSmartPointer<vtkActor>::New();
  actor->SetMapper(mapper);
  renderer->AddActor(actor);

  renderWindow->Render();
#endif

  return polydata->GetNumberOfPoints();
}
}

int TestLagrangeTetra(int argc, char* argv[])
{
#ifdef VISUAL_DEBUG
  vtkSmartPointer<vtkRenderWindow> renderWindow =
    vtkSmartPointer<vtkRenderWindow>::New();
  renderWindow->SetSize(500,500);

  vtkSmartPointer<vtkRenderWindowInteractor> renderWindowInteractor =
    vtkSmartPointer<vtkRenderWindowInteractor>::New();

  renderWindowInteractor->SetRenderWindow(renderWindow);
#endif

  int r = 0;

  // empirically determined values, verified visually
  static const vtkIdType nIntersections = 50;
  static const vtkIdType nClippedElems[11]= {0,6,9,33,45,85,91,26};

  vtkIdType nPointsForOrder[8] = {-1,4,10,20,35,56,84,15};

  for (vtkIdType order = 1; order <= 7; ++order)
    {
    vtkSmartPointer<vtkLagrangeTetra> t = CreateTetra(nPointsForOrder[order]);

#ifdef DEBUG_POINTS
      {
      vtkNew<vtkPolyData> p;
      p->SetPoints(t->GetPoints());
      vtkNew<vtkXMLPolyDataWriter> w;
      w->SetFileName("test.vtp");
      w->SetInputData(p.GetPointer());
      w->Write();
      }
#endif

    if (t->GetPoints()->GetNumberOfPoints() != 15)
      {
      for (vtkIdType i=0;i<t->GetPoints()->GetNumberOfPoints();i++)
        {
        vtkIdType bindex[4] = {static_cast<vtkIdType>(t->GetPoints()->GetPoint(i)[0]*order + .5),
                               static_cast<vtkIdType>(t->GetPoints()->GetPoint(i)[1]*order + .5),
                               static_cast<vtkIdType>(t->GetPoints()->GetPoint(i)[2]*order + .5),
                               0};
        bindex[3] = order - bindex[0] - bindex[1] - bindex[2];
        vtkIdType idx = t->ToIndex(bindex);
        if (i != idx)
          {
          std::cout<<"index mismatch for order "<<order<<"! "<<i<<" "<<idx<<std::endl;
          std::cout<<"bindex: "<<bindex[0]<<" "<<bindex[1]<<" "<<bindex[2]<<" "<<bindex[3]<<std::endl;
          std::cout<<"There are "<<t->GetPoints()->GetNumberOfPoints()<<" points"<<std::endl;
          return 1;
          }
        vtkIdType bindex_[4];
        t->ToBarycentricIndex(i,bindex_);
        if (bindex[0] != bindex_[0] || bindex[1] != bindex_[1] ||
            bindex[2] != bindex_[2] || bindex[3] != bindex_[3])
          {
          std::cout<<"barycentric index mismatch for order "<<order<<", index "<<i<<"! ("<<bindex[0]<<" "<<bindex[1]<<" "<<bindex[2]<<" "<<bindex[3]<<") vs "<<bindex_[0]<<" "<<bindex_[1]<<" "<<bindex_[2]<<" "<<bindex_[3]<<")"<<std::endl;
          return 1;
          }
        }
      }

    r += TestInterpolationFunction(t);
    if (r)
      {
      std::cout<<"Order "<<order<<" function failed!"<<std::endl;
      break;
      }
    r += TestInterpolationDerivs(t);
    if (r)
      {
      std::cout<<"Order "<<order<<" derivs failed!"<<std::endl;
      break;
      }

      {
      vtkMinimalStandardRandomSequence* sequence =
        vtkMinimalStandardRandomSequence::New();

      sequence->SetSeed(1);

      unsigned nTest = 5.e2;
      double radius = 1.5;
      double center[3] = {0.5,0.5,0.};
      vtkIdType nHits = IntersectWithCell(nTest,sequence,true,radius,center,t
#ifdef VISUAL_DEBUG
                                          ,renderWindow
#endif
                                          );

      sequence->Delete();

      r += (nHits == nIntersections) ? 0 : 1;

      if (r)
        {
        std::cout<<"Order "<<order<<" intersection failed!"<<std::endl;
        break;
        }
      }

      {
      vtkIdType nClippedElements = TestClip(t
#ifdef VISUAL_DEBUG
                                          ,renderWindow
#endif
);
      r += (nClippedElements == nClippedElems[order]) ? 0 : 1;

      if (r)
        {
        std::cout<<"Order "<<order<<" clip failed!"<<std::endl;
        break;
        }

      }
    }

#ifdef VISUAL_DEBUG
  for (vtkIdType i=testNum; i<16; i++)
  {
    vtkSmartPointer<vtkRenderer> renderer = vtkSmartPointer<vtkRenderer>::New();
    renderWindow->AddRenderer(renderer);
    double dim[4];
    ViewportRange(testNum++,dim);
    renderer->SetViewport(dim[0],dim[2],dim[1],dim[3]);
    renderer->SetBackground(0.,0.,0.);
  }

  renderWindowInteractor->Initialize();

  int retVal = vtkRegressionTestImage(renderWindow.GetPointer());
  if ( retVal == vtkRegressionTester::DO_INTERACTOR)
    {
    renderWindowInteractor->Start();
    retVal = vtkRegressionTester::PASSED;
    }

  r += (retVal == vtkRegressionTester::PASSED) ? 0 : 1;
#endif

  return r;
}
